In this thesis, a systematic study is carried out for effectively approximating Gerber-Shiu functions under L´evy subordinator models. It is a hardly touched topic in the recent literature and our approach is via the popular Fourier-cosine method. In theory, classical Gerber-Shiu functions can be expressed in terms of an infinite sum of convolutions, but its inherent complexity makes efficient computation almost impossible. In contrast, Fourier transforms of convolutions could be evaluated in a far simpler manner. Therefore, an efficient numerical method based on Fourier transform is pursued in this thesis for evaluating Gerber-Shiu functions. Fourier-cosine method is a numerical method based on Fourier transform and has been very popular in option pricing since its introduction. It then evolves into a number of extensions, and we here adopt its spirit to insurance risk theory. In this thesis, the proposed approximant of Gerber-Shiu functions under an L´evy subordinator model has O(n) computational complexity in comparison with that of O(n log n) via the usual numerical Fourier inversion. Also, for Gerber-Shiu functions within the proposed refined Sobolev space, an explicit error bound is given and error bound of this type is seemingly absent in the literature. Furthermore, the error bound for our estimation can be further enhanced under extra assumptions, which are not immediate from Fang and Oosterlee’s works. We also suggest a robust method on the estimation of ruin probabilities (one special class of Gerber-Shiu functions) based on the moments of both claim size and claim arrival distributions. Rearrangement inequality will also be adopted to amplify the use of our Fourier-cosine method in ruin probability, resulting in an effective global estimation. Finally, the effectiveness of our result will be further illustrated in a number of numerical studies and our enhanced error bound is apparently optimal in our demonstration; more precisely, empirical evidence exhibiting the biggest possible error convergence rate agrees with our theoretical conclusion. / published_or_final_version / Mathematics / Master / Master of Philosophy

The goal of this dissertation is to illustrate the importance and feasibility of conducting policy evaluations which pay attention to both efficiency and equity. Introducing an equity criterion necessarily involves introducing value judgements, but I suggest that objectivity can be maintained through the adoption of an 'ethically flexible' approach. That is, an analyst can avoid imposing his own particular values by explicitly conducting the evaluation from a number of different ethical positions. This dissertation illustrates the feasibility of an ethically flexible approach by carrying out an evaluation of the proposals for the reform of the Canadian Unemployment Insurance (UI) programme made by the Macdonald and Forget Commissions. The evaluation proceeds in four stages: 1. Behavioural models which take account of the existence of unemployment and UI are developed. 2. The models are estimated using an appropriate Canadian data set. 3. The estimated models are used to simulate behavioural responses to UI reform. 4. Estimation and simulation results are used to carry out the ethically flexible welfare evaluation. Two household labour-supply models are used. The first assumes that observed unemployment is the outcome of utility-maximizing choices. The second introduces the possibility that demand-side constraints may interfere with supply-side choices. A form of switching regression with sample separation unknown is developed to allow estimation of 'constrained' labour-supply functions. Additional problems for estimation include a budget constraint which is non-linear as a result of the UI programme and a dependent variable, weeks of leisure (unemployment), which is limited to values between zero and fifty-two. Both unconstrained and constrained models are estimated for single men, single women and couples, using linear expenditure systems and data from the 1982 Survey of Consumer Finance. Estimation results suggest that constrained labour-supply functions are less elastic than unconstrained functions, that there is no observable difference between the labour-supply behaviour of men and women in a constrained model, and that cross-effects are important in the determination of the labour-supply behaviour of couples. Estimated probabilities of constraint take an average value of (approximately) 80 percent. The simulation of behavioural responses to UI reform using the estimated unconstrained labour-supply functions suggests that large reductions in unemployment might be anticipated. Simulation using the constrained labour-supply functions suggests that responses may be negligible. Welfare evaluation measures are constructed for three ethical perspectives: The first is in the spirit of Utilitarianism; the second is in the spirit of John Rawls' theory of justice; the third is in the spirit of Robert Nozick's entitlement theory. The 'Utilitarian' measure is a mean of order r over the distribution of individual utilities. (Explicit interpersonal comparisons are required for these evaluations.) The 'Rawlsian' measure is a mean of order r over the distribution of individual incomes, censored at the poverty line to focus attention on the worst-off group. The 'Entitlement' measure is a measure of the distance between the distribution of individual costs (premiums) and benefits derived from UI. Three factors are important in the- determination of the welfare-evaluation results. First, the ethical position adopted matters. Both UI reform proposals appear welfare-reducing from a Utilitarian perspective and welfare-improving from an Entitlement perspective. Second, for the Rawlsian and Utilitarian evaluations, the assumed degree of inequality aversion is important. Finally, assumptions made about the nature of unemployment are critical. This is most clearly illustrated by the Rawlsian results. If unemployment is assumed to be the outcome of utility-maximizing choices, then both reform proposals appear welfare-improving: poor people choose to work more and their incomes increase. If unemployment may be the result of demand-side constraints so that increases in employment are not possible, then UI reform merely results in reductions in income for the worst-off group. These results illustrate the importance of both the equity and the efficiency dimensions of a policy evaluation. This thesis demonstrates the feasibility of conducting an objective policy evaluation which pays attention to both. / Arts, Faculty of / Vancouver School of Economics / Graduate

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

This dissertation consists of three essays: (I) Double Liability, Moral Hazard and Deposit Insurance Schemes, (II) Contract Costs, Lender Identity and Bank Loan Pricing, and (III) Bank Capital Structure and Differential Lending Behaviour. The first essay proposes to add double liability to a deposit insurance scheme to induce insurees (depository financial institutions) to reveal their true risk types. The second essay looks at the differential lending patterns of American banks versus Japanese banks. The third essay discusses the relationship between the characteristics of a lender and those of the borrower.

No description available.

Thesis (MSc)--Stellenbosch University, 2015 / ENGLISH ABSTRACT : Equity-based insurance guarantees also known as unit-linked annuities are annuities with embedded exotic, long-term and path-dependent options which can be categorised into variable and equity indexed annuities, whereby investors participate in the security markets through insurance companies that guarantee them a minimum of their invested premiums. The difference between the financial options and options embedded in equity-based policies is that financial ones are financed by the option buyers’ premiums, whereas options of the equity-based policies are financed by also continuous fees that follow the premium paid first by the policyholders during the life of the contracts. Other important dissimilarities are that equity-based policies do not give the owner the right to sell the contract, and carry not just security market related risk, but also insurance related risks such as the selection rate, behavioural, mortality, others and the systematic longevity. Thus equity-based annuities are much complicated insurance products to precisely value and hedge. For insurance companies to successfully fulfil their promise of eventually returning at least initially invested amount to the policyholders, they have to be able to measure and manage risks within the equity-based policies. So in this thesis, we do fair pricing of the variable and equity indexed annuities, then discuss management of financial market and insurance risks management. / AFRIKAANSE OPSOMMING : Aandeel-gebaseerde versekering waarborg ook bekend as eenheid-gekoppelde annuiteite is eksotiese, langtermyn-en pad-afhanklike opsies wat in veranderlike en gelykheid geindekseer annuiteite, waardeur beleggers neem in die sekuriteit markte deur middel van versekering maatskappye wat waarborg hulle ’n minimum van geklassifiseer kan word hulle belˆe premies. Die verskil tussen die finansi¨ele opsies en opsies is ingesluit in aandele-gebaseerde beleid is dat die finansi¨ele mense is gefinansier deur die opsie kopers se premies, terwyl opsies van die aandele-gebaseerde beleid word deur ook deurlopende fooie wat volg op die premie wat betaal word eers deur die polishouers gefinansier gedurende die lewe van die kontrakte. Ander belangrike verskille is dat aandele-gebaseerde beleid gee nie die eienaar die reg om die kontrak te verkoop, en dra nie net markverwante risiko sekuriteit, maar ook versekering risiko’s, soos die seleksie koers, gedrags, sterftes, ander en die sistematiese langslewendheid. So aandeel-gebaseerde annuiteite baie ingewikkeld versekering produkte om presies waarde en heining. Vir versekeringsmaatskappye suksesvol te vervul hul belofte van uiteindelik ten minste aanvanklik belˆe bedrag terug te keer na die polishouers, hulle moet in staat wees om te meet en te bestuur risiko’s binne die aandeel-gebaseerde beleid. So in hierdie tesis, ons doen billike pryse van die veranderlike en gelykheid geïndekseer annuiteite, bespreek dan die bestuur van finansiele markte en versekering risiko’s bestuur.

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

The insurance industry relies on both commercial and in-house software packages to quantify financial risk to natural hazards. For earthquakes, the initial loss estimates from the industry’s catastrophe risk (CAT) models are based on the probabilistic damage a building would sustain due to a catalog of simulated earthquake events. Based on the occurrence rates of the simulated earthquake events, an exceedance probability (EP) curve is calculated, which provides the probability of exceeding a specific loss threshold. Initially these loss exceedence probabilities help a company decide what insurance policies are most cost efficient. In addition they can also provide insights into loss predictions in the event that an actual natural disaster takes place, thus the insurance company is prepared to pay out their insured parties the necessary amount. However, there is always an associated uncertainty with the loss calculations produced by these models. The goal of this research is to reduce this uncertainty by using Bayesian inference with real time earthquake data to calculate an updated loss. Bayes theory is an iterative process that modifies the loss distribution with every piece of incoming information. The posterior updates are calculated by multiplying a baseline prior distribution with a likelihood function and normalization factor. The first prior is the initial loss distribution from the simulated events database before any information about a real earthquake is available. The crucial step in the update procedure is defining a likelihood function that establishes a relative weight for each simulated earthquake, relating how alike or dislike the attributes of a simulated earthquake are to those of a real earthquake event. To define this likelihood function, the general proposed approach is to quantify real time earthquake attributes such as magnitude, location, building tagging and damage, and compare them to an equivalent value for each simulated earthquake from the CAT model database. In order to obtain the simulated model parameters, the catastrophe risk model is analyzed for different building construction types, such as steel and reinforced concrete. For every model case, the loss, peak ground acceleration per building and simulated event magnitude and locations are recorded. Next, in order to calculate the real earthquake attributes, data was collected for three case studies, the 7.1 magnitude 1997 Punitaqui, the 8.8 magnitude 2010 Chile earthquake and the 6.7 magnitude 1994 Northridge earthquake. For each of these real earthquake events, the magnitude, location, peak ground acceleration at every available accelerometer location, building tagging and qualitative damage descriptions were recorded. Once the data was collected for both the real and simulated events, they were quantified so they could be compared on equal scales. Using the quantified parameter values, a likelihood function was defined for each update step. In general, as the number of updates increased, the loss estimates tended to converge to a steady value for both the medium and large event. In addition, the loss for the 6.7 and 7.1 event converged to a smaller value than that of the 8.8 event. The proposed methodology was only applied to earthquakes, but is broad enough to be applied to any type of peril.